I think persistence wouldn't help, but passion would, there's a difference between the two.
It helps the best if you've got something they want, i.e. they want you more than you want them. Like a particular skill-set (hence why they're always eager for more CS doctorates), otherwise they'll just poach someone from inside.
Developing good relationships with those inside also helps, especially when that person is high up, say... a product manager, since they're in charge of hiring for their team. If you're really good, you can bag an "Advocated" position, which (according to Sabot)
means you can forgoe the initial interview and get right in there.